The Electrical Trades Union has urged thousands of construction workers on billion-dollar Sydney building sites to attend an industry rally protesting the CFMEU administration, dismissing warnings it could be unlawful as “scaremongering”.

ETU NSW organisers visited Multiplex, Lendlease, Built and Mirvac projects on Monday, including the $5 billion federal government-funded Western Sydney Airport terminal, to promote a rally on Tuesday that is feared will grind the sector to a halt, industry sources said.